Electron Velocity Distribution Research Articles

Macroscopic plasma analysis from 1D-radial kinetic results of a Hall thruster discharge

A radial particle-in-cell model of the weakly-collisional plasma discharge in a Hall thruster, provides the non-Maxwellian velocity distribution functions (VDF) of ions and electrons. The model considers a radial magnetic field, secondary electron emission from the two walls, and phenomenological models of anomalous electron scattering. The electron VDF is used to assess the different terms in the macroscopic momentum and energy equations, identifying those differing from the standard fluid model for a near-Maxwellian VDF. The pressure tensor consists of an anisotropic gyrotropic part and a small gyroviscous part. Nonetheless, the gradient of this last one affects the cross-field electron current density, generating radial undulations that resemble those reported for near-wall conductivity. A gyroviscous energy flux is identified too. The heat flux parallel to the magnetic lines does not follow a conductive-type law but a convective-type one, already found in other weakly-collisional plasmas. The tails of the electron velocity distribution function are partially depleted due to wall collection, leading to reduced electron fluxes of particles and energy, which are characterized with parameters useful for fluid models. Differences in the plasma response for annular and planar channel geometries are highlighted. The levels of replenishment of the electron VDF and of the asymmetries in radial profiles differ for isotropic and anisotropic anomalous scattering models.

Nature and Variability of the Electron Velocity Distribution Functions and the Nonequilibrium Boltzmann Entropy in the Solar Wind at the First Lagrangian (L1) Point During the Halo CME Event on 25 July 2004

Nature and Variability of the Electron Velocity Distribution Functions and the Nonequilibrium Boltzmann Entropy in the Solar Wind at the First Lagrangian (L1) Point During the Halo CME Event on 25 July 2004

Computations of the multipole cross sections for directional excitation of ions by electron impact

A general relativistic distorted-wave expression of the multipole cross sections for anisotropic excitation of ions by impact with an electron beam is derived by taking into account the coherence between magnetic sublevels. These multipole cross sections are required in the analysis of the intensity and polarization of lines emitted from plasmas with cylindrically symmetric electron velocity distributions. To calculate such cross sections for highly charged target ions, we need to adapt the distorted-wave excitation program of the Flexible Atomic Code by making some modifications. Detailed computations are performed for transitions in the Be-like ion ${\mathrm{O}}^{4+}$ from the ground $2{s}^{2}$ and metastable triplet $2s2p$ levels. A selected series of results for transitions from $2s2p\phantom{\rule{0.16em}{0ex}}^{3}P_{1,2}$ to $2s3p\phantom{\rule{0.16em}{0ex}}^{3}P_{1,2}$ and $2s3d\phantom{\rule{0.16em}{0ex}}^{3}D_{2,3}$ levels, which may be of interest for the solar atmosphere and tokamak plasmas, are given to illustrate the application of the modified program suggested here. Indepth analysis of the numerical results and preliminary comparison with available data in the literature provide a systematic consistency of the modified program, paving the way for computations of a large amount of multipole cross sections's data with a considerable saving of time.

Electron Heat Flux in the Solar Wind: Generalized Approaches to Fluid Transport With a Variety of Skewed Velocity Distributions

AbstractIn the solar corona and solar wind, electron heat conduction is an important process that transports energy over large distances and helps determine the spatial variation of temperature. High‐density regions undergoing rapid particle‐particle collisions exhibit a heat flux described well by classical Spitzer‐Härm theory. However, much of the heliosphere is closer to a more collisionless state, and there is no standard description of heat conduction for fluid‐based (e.g., magnetohydrodynamic) models that applies generally. Some proposed models rely on electron velocity distributions that exhibit negative values of the phase‐space density. In this study, we explore how positive‐definite velocity distributions can be used in fluid‐based conservation equations for the electron heat flux along magnetic‐field lines in the corona and solar wind. We study both analytic forms of skewed distributions (e.g., skew‐normal distributions, two‐sided bi‐Maxwellians, and constant‐collision‐time electrostatic solutions) and empirical fits to measurements of core, halo, and strahl electrons in interplanetary space. We also present example solutions to a generalized conservation equation for the heat flux in the solar wind, with some limiting cases found to resemble known free‐streaming approximations. The resulting values of the electron heat flux vary as a function of radial distance and Knudsen number in ways that resemble observed data. We note that this model does not include the effects of kinetic instabilities (which may impose saturation limits when active), so for now its regime of applicability is limited to collisionless heat‐flux evolution away from the known instability boundaries in parameter space.

Multifractal wavefunctions of charge carriers in graphene with folded deformations, ripples, or uniaxial flexural modes: Analogies to the quantum Hall effect under random pseudomagnetic fields

The electronic behavior in graphene under arbitrary uniaxial deformations, such as foldings or flexural fields, is studied by including it in the Dirac equation pseudoelectromagnetic fields. General foldings are thus studied by showing that uniaxial deformations can be considered pseudomagnetic fields in the Coulomb gauge norm. This allows one to give an expression for the Fermi (zero) energy mode wavefunctions. For random deformations, contact is made with previous works on the quantum Hall effect under random magnetic fields, showing that the density of states has a power law behavior and that the zero energy mode wavefunctions are multifractal. This hints at an unusual electron velocity distribution. Also, it is shown that a strong Aharonov–Bohm pseudoeffect is produced. For more general nonuniaxial general flexural strain, it is not possible to use the Coulomb gauge. The results presented here helps to tailor-made graphene uniaxial deformations to achieve specific wavefunctions.

Evolution of electron cyclotron waves in a Hall-type plasma

A theoretical study of high-frequency electron waves in the plasma of a Hall-type discharge with crossed electric and magnetic fields is presented. The analysis of dispersion relations for a homogeneous weakly collisional plasma with the electron velocity distribution function obtained in the relaxation approximation is performed. It is shown that the nonequilibrium character of the electron distribution function can lead to kinetic instability of cyclotron waves. This instability occurs when the thermal velocity of electrons is comparable with the drift velocity in crossed fields. In the quasilinear approximation, a compact form of the diffusion coefficient of the distribution function in the velocity space is obtained, describing unstable modes' evolution and saturation. The analytical solutions are compared with the results of numerical simulation by the particle-in-cell method.

Generation of High-frequency Whistler Waves in the Earth’s Quasi-perpendicular Bow Shock

Abstract We use observations from the Magnetospheric Multiscale spacecraft to identify a free energy source for high-frequency whistler waves in the Earth’s quasi-perpendicular bow shock. In the considered measurements, whistlers propagate both parallel and antiparallel to the background magnetic field B 0 with frequencies around 100 Hz (0.15 f ce, where f ce is the electron cyclotron frequency) and amplitudes between 0.1 and 1 nT. Their growth can be attributed to localized pitch angle anisotropy in the electron velocity distribution function that cannot be precisely described by macroscopic parameters like heat flux or temperature anisotropy. However, the presence of heat flux along − B 0 does create preferential conditions for the high-frequency whistler waves that propagate in this direction. These waves are directed partially toward the shock, meaning they can scatter electrons that are streaming from the shock. This prolongs the time the electrons spend in the shock transition region and thereby promotes electron energization.

Measurability of the Nonlinear Response of Electron Distribution Function to Chorus Emissions in the Earth's Radiation Belt

AbstractWe conduct test particle simulations to study the perturbations in a hot electron velocity distribution caused by a rising chorus element propagating parallel to the ambient magnetic field in the Earth's outer radiation belt. The wavefield is constructed from the nonlinear growth theory of chorus emissions of Omura (2021, https://doi.org/10.1186/s40623-021-01380-w), with additional considerations about saturation and propagation of the transverse resonant current being applied to model the subpacket structure. Using Liouville's theorem, we trace electrons back in time to reconstruct the evolution of electron velocity distribution at the magnetic equator. The electromagnetic hole created by nonlinear trapping and transport effects appears as a depression in the velocity distribution, aligned with the resonance velocity curve. We analyze the decrease of particle flux in this depression and estimate the energy resolution, pitch angle resolution, time resolution and geometric factor of particle analyzers needed to observe the perturbation. We conclude that particle detectors on current or recently operating spacecraft are always lacking in at least one of these parameters, which explains the missing direct observations of sharp phase space density depressions during chorus‐electron nonlinear resonant interaction. However, with a dedicated experiment and appropriate measurement strategy, such observations are within the possibilities of the current technology. Similarity of the simulated density perturbation and a step function mathematical model is used to draw an analogy between the backward wave oscillator regime of chorus generation and the nonlinear growth theory.

On the Role of Solar Wind Expansion as a Source of Whistler Waves: Scattering of Suprathermal Electrons and Heat Flux Regulation in the Inner Heliosphere

Abstract The role of solar wind expansion in generating whistler waves is investigated using the EB-iPic3D code, which models solar wind expansion self-consistently within a fully kinetic semi-implicit approach. The simulation is initialized with an electron velocity distribution function modeled after observations of the Parker Solar Probe during its first perihelion at 0.166 au, consisting of a dense core and an antisunward strahl. This distribution function is initially stable with respect to kinetic instabilities. Expansion drives the solar wind into successive regimes where whistler heat flux instabilities are triggered. These instabilities produce sunward whistler waves initially characterized by predominantly oblique propagation with respect to the interplanetary magnetic field. The excited waves interact with the electrons via resonant scattering processes. As a consequence, the strahl pitch angle distribution broadens and its drift velocity reduces. The strahl electrons are scattered in the direction perpendicular to the magnetic field, and an electron halo is formed. At a later stage, resonant electron firehose instability is triggered and further affects the electron temperature anisotropy as the solar wind expands. Wave–particle interaction processes are accompanied by a substantial reduction of the solar wind heat flux. The simulated whistler waves are in qualitative agreement with observations in terms of wave frequencies, amplitudes, and propagation angles. Our work proposes an explanation for the observations of oblique and parallel whistler waves in the solar wind. We conclude that solar wind expansion has to be factored in when trying to explain kinetic processes at different heliocentric distances.

Upper‐Hybrid Waves Driven by Meandering Electrons Around Magnetic Reconnection X Line

AbstractMagnetic reconnection is a fundamental process in collisionless space plasma environment, and plasma waves relevant to the kinetic interactions can have a significant impact on the multiscale behavior of reconnection. Here, we present Magnetospheric Multiscale (MMS) observations during an encounter of an X line of symmetric magnetic reconnection in the magnetotail. The X line is characterized by reversals of ion and electron jets and electromagnetic fields, agyrotropic electron velocity distribution functions (VDFs), and an electron‐scale current sheet. MMS observe large‐amplitude nonlinear upper‐hybrid (UH) waves on both sides of the neutral line, and the wave amplitudes have highly localized distribution along the normal direction. The inbound meandering electrons drive the UH waves, releasing the free energy stored from the reconnection electric field along the meandering trajectories. The interaction between the meandering electrons and the UH waves may modify the balance of the reconnection electric field around the X line.

COMPUTER CALCULATION OF PROBABILITY FOR BINARY COLLISIONS OF ELECTRONS WITH IONS AND MOLECULES

Computer calculation of rate coefficient for binary collision i <σix> as a function of temperature is presented, and the Maxwell electron velocity distribution function is chosen. The finite elements of the fifth order made it possible to significantly speed up the process of calculation i <σix>. The result of the approximation is a smooth function and the values of this function, its first and second derivatives, have no jumps at the mesh nodes and the accuracy of calculation is within the limits of statistical errors for the source data. These advantages and the results will be used in future tasks.

Unipolar terahertz pulse formation in a nonequilibrium plasma channel formed by an ultrashort uv laser pulse.

We perform an alternative approach to produce highly unipolar terahertz pulses. The idea is based on the nonuniform amplification of seed ultrashort carrier-envelope phase (CEP) pulses in nonequilibrium fast relaxing plasma of air or nitrogen. If the gain coefficient drops significantly within the duration of a one-cycle CEP pulse, it undergoes significant distortion where the leading edge of the pulse is amplified and the trailing tail of opposite polarity is absorbed. The obtained results involve a self-consistent solution of the second-order wave equation and kinetic Boltzmann equation for the electron velocity distribution function relaxation.

Statistical analysis of non-Maxwellian electron distribution functions measured with angularly resolved Thomson scattering

Angularly resolved Thomson scattering is a novel extension of Thomson scattering, enabling the measurement of the electron velocity distribution function over many orders of magnitude. Here, details of the theoretical basis of the technique and the instrument designed for this measurement are described. Angularly resolved Thomson-scattering data from several experiments are shown with descriptions of the corresponding distribution functions. A reduced model describing the distribution function is given and used to perform a Monte Carlo analysis of the uncertainty in the measurements. The electron density and temperature were determined to a precision of 12% and 21%, respectively, on average, while all other parameters defining the distribution function were generally determined to better than 20%. It was found that these uncertainties were primarily due to limited signal to noise and instrumental effects. Measurements with this level of precision were sufficient to distinguish between Maxwellian and non-Maxwellian distribution functions.

New method of unipolar THz pulse generation in photo-ionised xenon plasma

We propose a new method for producing terahertz (THz) pulses with a high degree of unipolarity. This idea is based on the nonuniform amplification of seed THz one-cycle carrier envelope phase pulses in nonequilibrium xenon plasma. The significant impact of the propagated pulse on the evolution of plasma leads to a strong decrease in the gain coefficient within the duration of the one-cycle pulse. As a result, the leading edge of the pulse is amplified while the trailing tail of opposite polarity is absorbed; this effect leads to the formation of unipolarity. These results are obtained by the self-consistent solution of the second-order wave equation and kinetic Boltzmann equation for the electron velocity distribution function relaxation.

Simulation of Space-Charge-Limited Current for Hot Electrons With Initial Velocity in a Vacuum Diode

In this article, a sheet model is utilized to model and simulate hot electron transport properties in vacuum gap. Based on this model, emitted electrons with constant initial velocities and Maxwell–Boltzmann distribution are considered. Numerical analyses of the potential, electric field, current density, velocity, and phase-space distribution are also performed. The accuracy of this model is verified by comparing with analytical results. Furthermore, we studied the velocity distribution of the emitted electrons at any position in the interelectrode gap and observed a significant change in the distribution.

Electron Heat Flux Instabilities in the Inner Heliosphere: Radial Distribution and Implication on the Evolution of the Electron Velocity Distribution Function

Abstract This Letter investigates the electron heat flux instability using the radial models of the magnetic field and plasma parameters in the inner heliosphere. Our results show that both the electron acoustic wave and the oblique whistler wave are unstable in the regime with large relative drift speed (ΔV e ) between electron beam and core populations. Landau-resonant interactions of electron acoustic waves increase the electron parallel temperature that would lead to suppressing the electron acoustic instability and amplifying the growth of oblique whistler waves. Therefore, we propose that the electron heat flux can effectively drive oblique whistler waves in an anisotropic electron velocity distribution function. This study also finds that lower-hybrid waves and oblique Alfvén waves can be triggered in the solar atmosphere, and that the former instability is much stronger than the latter. Moreover, we clarify that the excitation of lower-hybrid waves mainly results from the transit-time interaction of beaming electrons with resonant velocities v ∥ ∼ ω/k ∥, where ω and k ∥ are the wave frequency and parallel wavenumber, respectively. In addition, this study shows that the instability of quasi-parallel whistler waves can dominate the regime with medium ΔV e at the heliocentric distance nearly larger than 10 times of the solar radius.

Measurements of Non-Maxwellian Electron Distribution Functions and Their Effect on Laser Heating.

Electron velocity distribution functions driven by inverse bremsstrahlung heating are measured to be non-Maxwellian using a novel angularly resolved Thomson-scattering instrument and the corresponding reduction of electrons at slow velocities results in a ∼40% measured reduction in inverse bremsstrahlung absorption. The distribution functions are measured to be super-Gaussian in the bulk (v/v_{th}<3) and Maxwellian in the tail (v/v_{th}>3) when the laser heating rate dominates over the electron-electron thermalization rate. Simulations with the particle code quartz show the shape of the tail is dictated by the uniformity of the laser heating.

Plasma Modeling and Prebiotic Chemistry: A Review of the State-of-the-Art and Perspectives.

We review the recent progress in the modeling of plasmas or ionized gases, with compositions compatible with that of primordial atmospheres. The plasma kinetics involves elementary processes by which free electrons ultimately activate weakly reactive molecules, such as carbon dioxide or methane, thereby potentially starting prebiotic reaction chains. These processes include electron–molecule reactions and energy exchanges between molecules. They are basic processes, for example, in the famous Miller-Urey experiment, and become relevant in any prebiotic scenario where the primordial atmosphere is significantly ionized by electrical activity, photoionization or meteor phenomena. The kinetics of plasma displays remarkable complexity due to the non-equilibrium features of the energy distributions involved. In particular, we argue that two concepts developed by the plasma modeling community, the electron velocity distribution function and the vibrational distribution function, may unlock much new information and provide insight into prebiotic processes initiated by electron–molecule collisions.

Inverse Bremsstrahlung absorption coefficient in inhomogeneous plasma with nonextensive electron velocity distribution and Tsallis exponential electron density profile

AbstractInverse bremsstrahlung (collisional) absorption of the laser beam is studied in plasma with a generalized (q‐nonextensive) electron velocity distribution and some kind of generalized electron density profile. It is shown that for some values of parameters designating the q‐nonextensive electron velocity distribution function and its generalized density profile, the calculated absorption coefficient reduces to the already known cases with Maxwellian velocity distribution with linear and exponential density profiles.

Laboratory measurements of the physics of auroral electron acceleration by Alfv\xe9n waves

While the aurora has attracted attention for millennia, important questions remain unanswered. Foremost is how auroral electrons are accelerated before colliding with the ionosphere and producing auroral light. Powerful Alfvén waves are often found traveling Earthward above auroras with sufficient energy to generate auroras, but there has been no direct measurement of the processes by which Alfvén waves transfer their energy to auroral electrons. Here, we show laboratory measurements of the resonant transfer of energy from Alfvén waves to electrons under conditions relevant to the auroral zone. Experiments are performed by launching Alfvén waves and simultaneously recording the electron velocity distribution. Numerical simulations and analytical theory support that the measured energy transfer process produces accelerated electrons capable of reaching auroral energies. The experiments, theory, and simulations demonstrate a clear causal relationship between Alfvén waves and accelerated electrons that directly cause auroras.